- #1

Zouatine

- 22

- 0

**hello everyone**

1. Homework Statement

1. Homework Statement

Problem:

An AB beam, loaded with a distributed load q (KN/m), the length of the beam is 2 m.

EI=constant

find the reactions in the beam ,we use

**y''=-(1/EI) *M(x)**

## Homework Equations

y''=-(1/EI) *M(x)[/B]

## The Attempt at a Solution

first we have 6 reactions (Va,Ha,Ma,Vb,Hb,Mb) in the supports.

∑F/x=0→ Ha+Hb=0 ,

**Ha=-Hb=0 -------------1**

∑F/y=0→ Va+Vb-Q=0 → Va+Vb=Q→ Va+Vb=∫ ((e^x)+(e^-x))dx 0≤ x ≤2

**Va+Vb= 7,25 KN -------------2**

∑M/b=0 → 2*Va- Q*(center of gravity of the load q)-Ma+Mb=0

center of gravity of the load q = (∫∫x*ds)/(∫∫ds)

∫∫x*ds= ∫∫x*dx*dy 0≤y≤(e^x)+(e^-x) , 0≤x≤2

∫∫x*ds= ∫∫x*dx*dy = 9,25 KN*m

∫∫ds= 7,25 KN

center of gravity of the load q = (∫∫x*ds)/(∫∫ds)=1,28 m (2-1,28)= 0,72m

2*Va- Q*0,72-Ma+Mb=0

**2*Va-Ma+Mb=5,22 KN m----------3**

Differential equation:

y''=-(1/EI) *M(x)

M(x) = ?? 0≤x<2

**my problem is how to find the moment equation?**

thanx